Contemporary Mathematics, Volume: 519
2010; 230 pp; softcover
ISBN-13: 978-0-8218-4929-3
Expected publication date is August 28, 2010.
This volume contains the proceedings of the Workshop on Homotopy Theory of Function Spaces and Related Topics, which was held at the Mathematisches Forschungsinstitut Oberwolfach, in Germany, from April 5-11, 2009.
This volume contains fourteen original research articles covering a broad range of topics that include: localization and rational homotopy theory, evaluation subgroups, free loop spaces, Whitehead products, spaces of algebraic maps, gauge groups, loop groups, operads, and string topology.
In addition to reporting on various topics in the area, this volume is supposed to facilitate the exchange of ideas within Homotopy Theory of Function Spaces, and promote cross-fertilization between Homotopy Theory of Function Spaces and other areas. With these latter aims in mind, this volume includes a survey article which, with its extensive bibliography, should help bring researchers and graduate students up to speed on activity in this field as well as a problems list, which is an expanded and edited version of problems discussed in sessions held at the conference. The problems list is intended to suggest directions for future work.
Graduate students and research mathematicians interested in properties of function spaces.
Survey article
S. B. Smith -- The homotopy theory of function spaces: A survey
Contributed articles
U. Buijs -- Upper bounds for the Whitehead-length of mapping spaces
D. Chataur -- String topology of classifying spaces and gravity algebras
M. C. Crabb -- A fibrewise stable splitting and free loops on projective spaces
Y. Felix and D. Tanre -- Rational homotopy of symmetric products and spaces of finite subsets
J.-B. Gatsinzi -- Derivations, Hochschild cohomology and the Gottlieb group
J.-B. Gatsinzi and R. Kwashira -- Rational homotopy groups of function spaces
J. Giansiracusa and P. Salvatore -- Formality of the framed little 2-discs operad and semidirect products
M. Golasi?ski, D. Goncalves, and P. Wong -- James construction, Fox torus homotopy groups and Hopf invariants
A. Kono and S. Tsukuda -- Notes on the triviality of adjoint bundles
A. Kozlowski and K. Yamaguchi -- Spaces of algebraic maps from real projective spaces into complex projective spaces
K. Kuribayashi -- On the rational cohomology of the total space of the universal fibration with an elliptic fibre
J. Oprea and J. Strom -- On the realizability of Gottlieb groups
C. L. Schochet and S. B. Smith -- Localization of grouplike function and section spaces with compact domain
C. Wockel -- Non-integral central extensions of loop groups
Problem list
Y. Felix -- Problems on mapping spaces and related subjects
2010; 319 pp; softcover
ISBN-13: 978-1-57146-141-4
Classical modular forms on the upper half plane, with respect to the modular group mathrm{SL}(2,mathbb{Z}) and its congruence subgroups, have arisen naturally in number theory, complex analysis, topology, mathematical physics, and many other subjects. The closely related automorphic representations are basic notions in the celebrated Langlands program, which was proposed by Langlands in the late 1960s and has since revolutionized the fields of number theory, arithmetic algebraic geometry, and representation theory. This volume consists of expanded lecture notes from a 2007 international conference in Guangzhou, China, at which several leading experts in number theory presented introductions to, and surveys of, many aspects of automorphic forms and the Langlands program.
Readership
Graduate students and research mathematicians interested in the Langlands program.
Table of Contents
A. W. Knapp -- Prerequisites for the Langlands program
A. W. Knapp -- First steps with the Langlands program
S. S. Gelbart -- Class field theory, the Langlands program and its application to number theory
W. T. Gan -- Automorphic forms and automorphic representations
E. M. Lapid -- Introductory notes on the trace formula
S. Friedberg -- Euler products and twisted Euler products
X. Li -- Arithmetic trace formulas and Kloostermania
D. Shelstad -- Tempered endoscopy for real groups II: Spectral transfer factors
L. Guo -- Algebraic Birkhoff decomposition and its applications
2010; 527 pp; softcover
ISBN-13: 978-1-57146-142-1
In a career of nearly sixty years of mathematical research, Guangchang Dong's influence on the development of partial differential equations in China has been immense, at both the teaching and research levels. To celebrate his eightieth birthday, an international conference called Elliptic and Parabolic Equations and Applications was held in August 2008 at Zhejiang University in Hangzhou, China. This volume presents fifteen papers, some drawn from lectures given at the conference and others by his friends and former students.
Readership
Graduate students and research mathematicians interested in partial differential equations.
Table of Contents
B. Bian and Y. Wang -- Viscosity solutions of Bellman equations arising in pricing passport options
K.-S. Chou and S.-Z. Du -- On global partial regularity for borderline solutions of semilinear parabolic problems
B. Guan -- The Dirichlet problem for complex Monge-Ampere equations and applications
Y. Han and G. Lu -- Some recent works on multiparameter Hardy space theory and discrete Littlewood-Paley analysis
M.-C. Hong -- Some analytic aspects of liquid crystal configurations
D.-X. Kong -- Extremal sub-manifolds in Minkowski space-time
J. Ling and Z. Lu -- Bounds of eigenvalues on Riemannian manifolds
Y. Lu -- Wave breaking phenomena and stability of peakons for the Degasperis-Procesi equation
X.-N. Ma and Q. Ou -- The convexity of level sets for solutions to partial differential equations
X.-B. Pan -- Nucleation of instability of Meissner state of superconductors and related mathematical problems
Y.-B. Shen -- Calculus of some geometric variations in Finsler geometry
W. Sheng and X.-J. Wang -- Regularity and singularity in the mean curvature flow
L. Shen and G. Lv -- Study of finite point method
J. Yin, P. Lei, and C. Wang -- Nonlinear diffusion equations with different kind of degeneracy
X. Zhu -- Canonical metrics on toric manifolds
List of publications by Guangchang Dong
2010; 229 pp; softcover
ISBN-13: 978-1-57146-143-8
This volume presents an account of recent advances in geometric analysis and related topics, including Ricci flow, affine normal flow, geometric analysis on pseudo-convex hypersurfaces, Alexandrov space, manifolds with special holonomy, and the singular plateau problem. These papers, many by leading experts in the field, are drawn from lectures presented at the 2007 International Conference in Geometric Analysis, held at Taiwan University. The present volume is intended for both researchers and graduate students studying geometric analysis and related areas.
Graduate students and research mathematicians interested in geometric analysis.
H.-D. Cao -- Recent progress on Ricci solitons
J. Cao, B. Dai, and J. Mei -- An optimal extension of Perelman's comparison theorem for quadrangles and its applications
D.-C. Chang and S. S.-T. Yau -- Geometric analysis on a family of pseudoconvex hypersurfaces
S. Ji -- A new proof for Faran's theorem on maps between B2 and B3
S. Karigiannis -- Some notes on G2 and Spin(7) geometry
L. Ni -- Closed type I ancient solutions to Ricci flow
J. Loftin and M.-P. Tsui -- Limits of solutions to a parabolic Monge-Ampere equation
C.-S. Lin and C.-L. Wang -- A function theoretic view of the mean field equations on tori
S.-C. Lau and N. C. Leung -- Conformal geometry and special holonomy
L.-F. Tarn -- Exhaustion functions on complete manifolds
S. Yamada -- On singular plateau problem
2010; 517 pp; softcover
ISBN-13: 978-1-57146-144-5
Cohomology of groups is a fundamental tool in many subjects of modern mathematics. One important generalized cohomology theory is the algebraic K-theory. Indeed, algebraic K-groups of rings are important invariants of the rings and have played important roles in algebra, topology, number theory, etc. This volume consists of expanded lecture notes from a 2007 seminar at Zhejiang University in China, at which several leading experts presented introductions to and surveys of many aspects of cohomology of groups and algebraic K-theory, along with their broad applications. Two foundational papers on algebraic K-theory by Daniel Quillen are also included.
Graduate students and research mathematicians interested in cohomology of groups and algebraic K-theory.
A. Bartels and W. Luck -- On crossed product rings with twisted involutions, their module categories and L-theory
O. Baues -- Deformation spaces for affine crystallographic groups
K. S. Brown -- Lectures on the cohomology of groups
D. R. Grayson -- A brief introduction to algebraic K-theory
D. Juan-Pineda and S. Millan-Lopez -- The braid groups of RP2 satisfy the fibered isomorphism conjecture
M. Karoubi -- K-theory, an elementary introduction
M. Karoubi -- Lectures on K-theory
W. Luck -- On the Farrell-Jones and related conjectures
S. Prassidis -- Introduction to controlled topology and its applications
H. Qin -- Lecture notes on K-theory
D. Quillen -- Higher algebraic K-theory: I
D. Quillen -- Finite generation of the groups K_i of rings of algebraic integers
D. Rosenthal -- A user's guide to continuously controlled algebra
C. Soule -- Higher K-theory of algebraic integers and the cohomology of arithmetic groups (Notes by M. Varisco